Related papers: Analysis and Predictability for Tipping Points wit…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to…

It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…

We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…

In the prediction of oscillating time series, the interest is in the turning points of successive oscillations rather than the samples themselves. For this purpose a scheme has been proposed; the state space reconstruction is limited to the…

A variety of real world and experimental systems can display a drastic regime shift, as the evolution in one its paramaters crosses a threshold value. Assimilation of such a transition with a bifurcation has allowed to identify so called…

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…

Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard…

A tipping point can be defined as an abrupt shift in the properties or behaviour of a system. Tipping points in complex systems from a wide variety of scientific disciplines have been compared to phase transitions in physics, but consistent…

Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series…

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…

In online classification, a learner is presented with a sequence of examples and aims to predict their labels in an online fashion so as to minimize the total number of mistakes. In the self-directed variant, the learner knows in advance…

In this work, we discuss how the linear and non-linear advection terms modify the scaling behavior of the continuous symmetry breaking and stabilize the long-range order, even in $d=2$ far from equilibrium, by means of simple scaling…

We present a non-linear stability analysis of quasi-static slip in a spring-block model. The sliding interface is governed by rate- and state-dependent friction, with an intermediate state evolution law that spans between aging and slip…

The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are…

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…